The mathematical expression of the rate of reaction on concentration terms of reactants is known as rate expression or rate equation or rate law.

For reaction \(A + B \rightarrow Products\), the rate equation is

\[rate ­\propto [A] [B]\]

\[rate = K [A] [B]\]

K is known as specific rate constant or rate per unit concentration of the reactants.

Units of rate constant are \((mole)^{1−n} (litre)^{n−1} s^{−1}\).

Rate law for any reaction cannot be predicted by looking at the balanced chemical reaction, that is, theoretically but must be determined experimentally.

Several chemical reactions take place in a sequence

of steps and the overall rate of reaction is governed

by the slowest step.

In certain cases, the slowest or rate-determining step may involve the formation of an unstable intermediate

from the reactant molecules. The total number of reactant molecules taking part in the slowest step may involve the formation of an unstable intermediate. The total number of reactant molecules taking part in the slowest step or limiting step in the formation of intermediate species is known as the molecularity of the reaction.

Which of the following statement is false?

The acid-catalysed hydrolysis of ester is second- order reaction

The correct answer is option 3. The acid-catalysed hydrolysis of ester is second- order reaction.

Let us examine each statement to identify the false one:

1. Radioactive decay follows first-order kinetics.

This statement is generally true. Radioactive decay typically follows first-order kinetics, meaning the rate of decay is proportional to the amount of radioactive substance remaining.

2. \(T_{1/2}\) for a zero-order reaction is proportional to the initial concentration \(a\).

This statement is true. In a zero-order reaction, the half-life is directly proportional to the initial concentration of the reactant. As the initial concentration increases, the half-life also increases proportionally.

3. The acid-catalyzed hydrolysis of ester is a second-order reaction.

This statement is false. The acid-catalyzed hydrolysis of an ester is typically a first-order reaction, not a second-order one. It proceeds through a unimolecular mechanism, meaning the rate-determining step involves only one molecule (the ester).

4. The units of the rate constant are \((\text{mole})^{1-n}(\text{litre})^{n-1}\text{s}^{-1}\).

This statement is also true. The units of the rate constant \(k\) depend on the order of the reaction. For a general reaction \(aA + bB \rightarrow cC + dD\), the units of \(k\) are \((\text{concentration})^{1-n}(\text{time})^{-1}\), where \(n\) is the order of the reaction. For a first-order reaction, \(n = 1\), so the units become \((\text{mole})^{1-1}(\text{litre})^{1-1}\text{s}^{-1}\), which simplifies to \(\text{s}^{-1}\).

The false statement is:3. The acid-catalyzed hydrolysis of ester is a second-order reaction.